1. The problem statement, all variables and given/known data Find the number of zeroes of p(z) = z^5 + 10z - 1 inside |z| < 1 2. Relevant equations 3. The attempt at a solution Let f(z) = z^5 g(z) = 10z-1 On |z| = 1: 10|z| - 1< |10z-1| < 10|z| + 1 (is this true...?) 9 < |g(z)| < 11 |f(z)| = 1 So |g| > |f|, so f+g should have the same number of zeroes as f, which is five. That's incorrect obviously. What am I doing wrong?